The geometry of cognition: from neural populations to neurotechnology

Cognition is implemented by distributed neural populations whose collective activity evolves through structured, low-dimensional state spaces. In this review, we survey the analytical and conceptual tools used to study latent population dynamics in biological neural networks. We begin with single-unit coding, which remains essential for interpreting neuronal selectivity, and then review population-level approaches, including population vectors, cosine similarity, principal component analysis and its mnemonic variants, multivariable linear regression axes, demixed principal component analysis, and single-trial latent-variable models, and distinguish operationally defined population subspaces from neural manifolds with reproducible geometry or topology. We use these methods to discuss sensory coding, working memory, decision-making, temporal processing, and sensorimotor transformations. Two organizing principles are emphasized throughout. First, cognitive variables can be expressed in separable or near-orthogonal population dimensions, reducing interference between sensory, mnemonic, decision-related, and motor signals. Second, such geometric separation does not require anatomically or functionally discrete cell classes; separable population readouts can coexist with a continuum of mixed-selective single-neuron responses within a shared biological substrate. We then consider recurrent neural networks as testbeds for generating and evaluating mechanistic hypotheses about how circuits produce low-dimensional dynamics, and intracortical brain-computer interfaces as a translational domain in which population geometry becomes an operational control signal. Overall, this review argues that population dynamics now provide a common language for linking neurophysiology, computational modelling, and neurotechnology.